IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 The Effect of Spot Size on the Fractal Optical Modulation A. A S Mohammad , K. H Harby , T.A. K Al-Aish Departme nt of Physics ,College of Education Ibn Al-Haitham ,Unive rsity of Baghdad Received in : 30, October , 2010 Accepte d in : 27, February, 2011 Abstract The present p aper analy zes the sign al emitt ing from t he Reticle during changing the sp ot size of laser fallin g on the disk and shows the optimum frequency and the amount of energy window in different p atterns of modulator (Reticle). All results are obtained by establishing a sp ecial p rogram named “Disk optical modulator version 3" usin g the lan guage visual b asic 6 ahich contains many p arameters. All models of op tical modulator consist of twenty sectors, ten sectors are op aque and other ten sectors are transmitted for the laser. The number of sectors dep ends on several factors as chopping frequen cy, p ower transp arent and modulation transfer function. It has been demonst rated by simulations, the op timal value of modulation transfer function is achiev ed when sp ot size of laser 0.3 mm and any increasin g in sp ot size lead to decrease in M TF value. Keywords: Fractal Op tical M odulator, Chopp ing frequency, Sp ot size, p ower transp arent, the M odulation Transfer Function MT F Introduction In any electro- op tical tracking sy stems the optical modulation disk (R eticle) is used as optical filter for back ground discrimination. The design and movement of the Reticle is to enhance the object and supp ress the background. The detection of Reticle is limited to p oint sources of radiation and to ach ieve the best efficien cy of the disk [1]. In p ractice, it must not exceed the size of R eticle sector at three times the size of target image. The ideal situation, in fact, occurs when the dimensions of object image is equal to the dimensions sectors Reticle, but the increase in the volume of object image as a result of the app roaching electro- optical sy stem is the real motive behind the reduced dimensions of its image in order to st art a third remove sections of Reticle, should not exceed ing the dimensions sp ot dimensions of disk sectors [2]. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Design of Reticle There are some factors of spot size affecting on the Reticle desi gn, usually the design of Reticle dep ends on the following [2, 3, 4]: 1. The nature of work of electro-optical sy stem (negative or p ositive mode). 2. The typ e and nature of the objects t o be p ursued and sources of ambient noise. 3. The dimensions of Reticle. 4. The rotation sp eed and the number of sectors of Reticle. 5. The requirements of t he sp eed of resp onse of the syst em. 6. The field of vision to be cover ed. 7. The nature of the electronic cir cuits used in sign al p rocessing The dimensional ideal for Reticle design whi ch is b ased on the p rogress of t he abov e factors will assume number of assumptions, in electro-op tical tracking sy stems with active mode, the target is illuminated by an external source of lighting, often the source is one type of lasers. Where the p rinciple in such sy st ems, is based on the tar get ( as a reflectin g surface diffuse typ e), thus the source represented as radiation source or lamb ertian source [4]. Since the p rop osed range of electro-opt ical tracking sy st ems is about 5 km therefore has been chosen one solid-state lasers (CW), which is Nd-Yag laser, high ener gy and wavelength (1.06 micrometers). T his wavelength is located within the limits of the op tical resp onse detector made of silicon with dist inctive characteristics and cheap p rice [5,6]. Two models has been designed for Reticle; the first design is normal way , so as to comp are the results obtained from this model with the results of the second model, which was design ed by using Fractal Function,( a new t echnique) [7,8]. The normal op tical modulator is a circular disc which has a radius R, which assumes the number of sector is (twenty sectors), ten sectors are op aque and the other ten sectors are transmitted for the light as shown in Fig (1). One may consider these ten sectors also as op aque for the other regions of electro -magnetic wave sp ectrum. By using this concept and IFS (I te ra te d Fu ncti on Sys te m) kit p rogram [9], we have designed optical modulator as shown in Fig (2). This op tical modulator consists of two p att ern circles. Each circle is divided into t en transp arents and ten opaque sectors (q). The first p att ern, is (inner p att ern) designed in a circle with data as shown in Table (1). Aft er conducting the op erations of scaling, rotation and iteration (for many times) the obtained p att ern is as shown in Fig (2). The second p att ern (outer p att ern) is designed in an equilateral triangle with data as shown in Table (2).Aft er (many times) of conducting the op erations of scaling, rotation and iteration, the result is as shown in Fig. (2). Re sult and Discussion To get work it has been established a sp ecial p rogram named “Disk optical modulator version 3" using the lan guage visual b asic 6 whi ch contains many p arameters and as shown in Table (3). When calculating the frequ ency it has been converted to units (Rev / s), as well as for angu lar velocity w, The Law of frequency is given by [10]: IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 2/wfr  ……..…. (1) qfrfc  …………. (2) Where fc chopp ing Frequency , fr rotation Frequency and q number of sectors. The basic idea in this research requir es exp ansion the sp ot size of laser to cover the full Reticle with radius equals to 90 mm and by assuming the p ower of laser emission from sourc e about PL= 50 Watt and diameter of sp ot is r = 3 mm with wavelength , and distribution of the p ower density in the near field given by [2, 11]: ………….. (3) for r = 1.5 mm When extended the sp ot laser to cover all effective area of reticle become for r = 90 mm The great p art of the laser ener gy will loss as a result of the p rocesses of reflection, absorption, and that will suffer, when p assed through the op tical comp onents of the transmitter unit, if the transmitt ance of the lens of an exp anded p ackage are and , its means lost 20% of the power energy in lens And app roximately 80% of the energy falls on a Reticle which have transp arent for transp arent sectors. The p ower transp arent P of each sector is given by the equation [2,11]: p = Sn τr …………………….(4) Where =0.729 and Sn area of sub sector The modulation transfer function M TF is calculated for each p att ern by calculating the transmittance intensity by using the equation:- minmax minmax II II MTF    Where: Im ax: is transmittance maximum intensity and Im in : is oblique minimum intensity .we calculate Imax (the ratio between the sp ot size and the transmittance area), and Im in (the ratio between the sp ot size and oblique area [12,13]. Then we measure the modulation transfer function M TF by using eq (5). The results that were obtained based on a number of infor mation assumed as shown in Table (4) and Table (5). First , we may draw the relationship between the rotation frequency and Chopp ing frequency with number of sectors, we got the curve shown in Fig(3) …… ……… ………….…….. (5) IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 The movement of any section in a circular motion takes app roximately 0.0001 seconds (for the disc consists of 10 sections of dark does not allow p assage of the power and 10 section window allows p assage p ower) that would lead to cut the signal on an on go ing basis every 0.0001 seconds as shown in Table ( 6 ) and Figs (4, 5), which represents the relationship between p ower transp arent and the time, also it shows, that the p ower transp arent is directly p rop ortional with size of sector, consequently the p ower transp arent from fractal Reticle is lar ger from normal R eticle. Changing spot size of laser Theoretically, the best detection occurs when sectors of the disk is determined p eriodically and the for ms and dimensions similar to the form and d imensions of sp ot, this leads to comp lete the modulation continues p rocess and reduce the frequency bandwidth occup ied by the optical signal to t he lowest extent p ossible, or in other words, reduce the impact of noise to a minimu m [2,9,8]. To exp lain the imp act of changing sp ot size of laser on the fractal modulator frequency, we will chan ge the sp ot size between 0.3 mm 2 to 0.6 mm 2 fro m ar ea of sector as shown in Table (7), and then evaluate the best value of M TF dep ending on Eq.5 In order to unify the values for all models we'll take st airs gr adually to cover these Valu es, dependin g on the minimum value (0.376 mm 2 ) and maximu m value (0.93 mm 2 ) and between them in the followin g mann er S pot size in mm 2 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 Tables (8, 9, 10 and 11) shows the results of the fc and modulation transfer function M TF which was obtained as a result of changing the sp ot size from 0.3 mm 2 to 0.6 mm 2 (as shown in Figure (6)to fi g.(13)). We note that the best value for the M TF was obtained when the size of the section is equal to 0.3 mm2 and any increase in sp ot size after this value leads to adverse ly affects on MT F for all models, and this supp orts what we assumed theoretically for the case of an ideal fit between the sp ot size and area of the section of the disk. Conclusion 1 - The outer p attern of fractal Reticle is used to detect the target , which requires that the aperture sizes are larger than the target by three times to achieve the followin g:  early detection of distant targets situated within the range of Reticle  The ability to detect more than on e objective, and d etermine the coordinates of based on its initial size and shap e  Keep the targets under monitorin g, esp ecially when approaching where the bigger size  Give adequate time for the reorientation of the visual sy st em in order to drop in body image exp osed on the inner pattern of fractal model by object-oriented lens. 2 - The inner pattern of fractal Reticle is used for the purp ose of the lock on the target, and this IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 requires that the exp ulsion of the target equals to the dimensions of sectors to achieve the followin g:  Complete the modulation continues p rocess and this leads to reduce the imp act of noise to a minimum.  Access to the regular si gnal and nearly constant frequency . 3. The p ower transp arent is directly p rop ortional with size of sector; consequently the p ower transp arent from fractal Reticle is lar ger from normal Reticle Re ferences 1. Harry , L. VAN TREES, (2001), Detection, Estimation, and M odulation Theory ", Book: George M ason University , ISBNs: 0-471-10793-X (Pap erback); 0-471-22109-0 (Electronic), Library of Congr ess, USA. 2. Reyad, N. Ali, (2004), Desi gn Study on Laser Guidance Sy st em Emp loying an Op tical Reticle, PH.D Thesis, Al- Rasheed College of engineering. 3. Hy un, K. Hong, Sun g, H . Han, Gy oung, P. Hon g, and Jong, S. Choi, (1996), Simu lation of Reticle Seek ers Using the Generated Thermal Images, Proceed ings I E E E Conf erence on Circuits and Sy st ems, Seoul. 4. M arvin, K. Simon, (2001), Bandwidth-Efficient Di gital M odulation with App lication to Deep-Sp ace Communications, Book, Publisher : Wiley , California Inst itut e of Technology 5. Biberman, L. M . (1966) Reticles in Electro-Op tical devices, ergamon Press, Published Pergamon Press in Oxford, Toronto. 6. Wolfe w, and Zissis G, (1978), The Infrared Handbook, IRIA center, Environmental research Institut e of M ichigan. 7. M andelbrot, B.B (1982),The Fractal Geometry of Nature. W.H. Freeman and Company.. ISBN 0-7167-1186-9, New York. 8. Thair, A.A.(2002), Fractal Image Sy nthesis by Iterated Function Sy stem, M Sc Thesis, University of Baghdad. 9. IFS kit program, http://ecademy .agnesscott.edu/~lriddle/ifskit/ 10. Gramm, C.F. (1965), Infrared Equip ment , Chapter 9 Volume Two of App lied Optics and Opt ical Engineering , R. kingsl ake editor, Academic. 11. George, M . Siouris, (2004), M issile Guidance and Control Sy st ems, ISBN 0-387-00726-1 (hc. : alk. p aper), Sp ringer, Verlag New York, Inc. 12. Fadl, W. (2004), Desi gn Op tical M odulator by Using Fractal Function Geometry , M Sc Thesis, Al-M ustansiry ah University. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 13. Ahmed, S.A. (2008), Calculation of M TF for Optical Disk M odulator by Using Fractal Function, M Sc Thesis, University of Technology . Table (1): The initial shape of the first pattern Table (2): The initial shape of the se cond pattern Table( 3) data of Di sk optical modul ator v.2 Program Table( 4): The results of normal and Reticle disk IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 State Nor mal Ret icle Fract al Ret icle Inner Patt ern Oute r Pattern radius 0.09 m 0.03 m 0.09 m Time 0.002 sec 0.002 sec 0.002 sec Number of sec tor 20 20 20 spot size of laser 0.5 mm 0.5mm 0.5 mm Angle of se ct or 18 degre e 18 degre e 18 degre e Circ umfe re nce 0.5652 m 0.1884 m 0.5652 m Ar ea of disk 0.025434 m2 0.002826 m2 0.025434 m2 Angular ve locity 1744.44 rad/sec 5233.33 rad/sec 1744.44 rad/sec Rotational fr equency 277.77 833.33rad/sec 277.77 Chopping fr equency 2777.7 rad/sec 8333.3 rad/sec 2777.7 rad/sec Table (5): data of sub se ctor for normal and fractal reti cle State Nor mal Ret icle Fract al Ret icle Inner Patt ern Oute r Pattern Circ umfe re nce sub sec tor 0.02826 m 0.1884 m 0.02826 m Ar ea of tr ansparent sub sec tor 0.0012717 m2 0.00001256m2 0.00001558842m2 Ar ea of tr ansparent sector 0.0012717 m2 0.001256m2 0.001558842m2 Table (6) : The power transparent of Reticle disk No of sector Time in sec Pow er tra nspa rent of Normal in Watt Pow er tra nsparent of inner fractal in wa tt Pow er tra nsparent of o ut er fra cta l in wat t 1. 0.0001 0 0 0 2. 0.0002 1.82 1.7999 2.234 3. 0.0003 0 0 0 4. 0.0004 1.82 1.7999 2.234 5. 0.0005 0 0 0 6. 0.0006 1.82 1.7999 2.234 7. 0.0007 0 0 0 8. 0.0008 1.82 1.7999 2.234 9. 0.0009 0 0 0 10. 0.001 1.82 1.7999 2.234 11. 0.0011 0 0 0 12. 0.0012 1.82 1.7999 2.234 13. 0.0013 0 0 0 14. 0.0014 1.82 1.7999 2.234 15. 0.0015 0 0 0 16. 0.0016 1.82 1.7999 2.234 17. 0.0017 0 0 0 18. 0.0018 1.82 1.7999 2.234 19. 0.0019 0 0 0 20. 0.002 1.82 1.7999 2.234 Table(7): data of (0.3 - 0.6 )area of sub sector for normal and fractal reticle IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Ar ea of tr ansparent sector 0.0012717m 2 0.001256m 2 0.001558842m 2 Outer pattern Inner pattern Normal reti cle Sp ot size State Sp ot size State Sp ot size State 0.00046 0.3 0.000376 0.3 0.000381 0.3 0.00062 0.4 0.0005024 0.4 0.000508 0.4 0.00073 0.5 0.000628 0.5 0.000635 0.5 0.00093 0.6 0.0007536 0.6 0.000763 0.6 Table(8 ):The MTf of Normal and fractal Reticle when S pot size = 0.0003 m Nor mal Ret icle Fract al Ret icle Inner Patt ern Oute r Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.7 0.096 0.03 8333.33 0.32 0.09 2777.7 0.96 0.018 13888.8 0.192 0.02906 8602.89 0.309 0.08720 2866.97 0.930 0.027 9259.25 0.288 0.026477 9442.15 0.282 0.0794 3148.61 0.846 0.036 6944.44 0.384 0.02287 10931.35 0.243 0.0686 3644.31 0.731 0.045 5555.55 0.48 0.01946 12846.86 0.207 0.05840 4280.82 0.622 0.054 4629.62 0.576 0.018 13888.88 0.192 0.054 4629.62 0.576 0.063 3968.25 0.672 0.01946 12846.86 0.207 0.05840 4280.82 0.622 0.072 3472.22 0.768 0.02287 10931.35 0.243 0.0686 3644.31 0.731 0.081 3086.41 0.864 0.026477 9442.15 0.282 0.0794 3148.61 0.846 0.09 2777.77 0.96 0.02906 8602.89 0.309 0.08720 2866.97 0.930 Table(9 ):The MTf of Normal and fractal Reticle when S pot size = 0.0004 Nor mal Ret icle Fract al Ret icle Inner Patt ern Oute r Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.075 0.03 8333.33 0.25 0.09 2777.77 0.75 0.018 13888.88 0.15 0.02906 8602.89 0.242 0.08720 2866.97 0.726 0.027 9259.25 0.225 0.026477 9442.15 0.22 0.0794 3148.61 0.661 0.036 6944.44 0.3 0.02287 10931.35 0.190 0.0686 3644.31 0.571 0.045 5555.55 0.375 0.01946 12846.86 0.162 0.05840 4280.82 0.486 0.054 4629.62 0.45 0.018 13888.88 0.15 0.054 4629.62 0.45 0.063 3968.25 0.525 0.01946 12846.86 0.162 0.05840 4280.82 0.486 0.072 3472.22 0.6 0.02287 10931.35 0.190 0.0686 3644.31 0.571 0.081 3086.41 0.675 0.026477 9442.15 0.22 0.0794 3148.61 0.661 0.09 2777.77 0.75 0.02906 8602.89 0.242 0.08720 2866.97 0.726 Table(10 ):The MTf of Normal and fractal Reticle when S pot size = 0.0005 Nor mal Ret icle Fract al Ret icle Inner Patt ern Oute r Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.06 0.03 8333.33 0.2 0.09 2777.77 0.6 0.018 13888.88 0.12 0.02906 8602.89 0.193 0.08720 2866.97 0.581 0.027 9259.25 0.18 0.026477 9442.15 0.176 0.0794 3148.61 0.529 0.036 6944.44 0.24 0.02287 10931.35 0.152 0.0686 3644.31 0.457 0.045 5555.55 0.3 0.01946 12846.86 0.129 0.05840 4280.82 0.389 0.054 4629.62 0.36 0.018 13888.88 0.12 0.054 4629.62 0.36 0.063 3968.25 0.42 0.01946 12846.86 0.129 0.05840 4280.82 0.389 0.072 3472.22 0.48 0.02287 10931.35 0.152 0.0686 3644.31 0.457 0.081 3086.41 0.54 0.026477 9442.15 0.176 0.0794 3148.61 0.529 0.09 2777.77 0.6 0.02906 8602.89 0.193 0.08720 2866.97 0.581 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Table(11):The MTf of Normal and fractal Reticle when S pot size = 0.0006 Normal Reticle Frac tal Reticle Inne r Patter n Outer Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.05 0.03 8333.33 0.166 0.09 2777.77 0.5 0.018 13888.88 0.1 0.02906 8602.89 0.161 0.08720 2866.97 0.484 0.027 9259.25 0.15 0.026477 9442.15 0.147 0.0794 3148.61 0.441 0.036 6944.44 0.2 0.02287 10931.35 0.127 0.0686 3644.31 0.381 0.045 5555.55 0.25 0.01946 12846.86 0.108 0.05840 4280.82 0.324 0.054 4629.62 0.3 0.018 13888.88 0.1 0.054 4629.62 0.3 0.063 3968.25 0.35 0.01946 12846.86 0.108 0.05840 4280.82 0.324 0.072 3472.22 0.4 0.02287 10931.35 0.127 0.0686 3644.31 0.381 0.081 3086.41 0.45 0.026477 9442.15 0.147 0.0794 3148.61 0.441 0.09 2777.77 0.5 0.02906 8602.89 0.161 0.08720 2866.97 0.484 Fig. (1): The Normal optical modulator Fig. (2): The fractal optical modul ator IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Fig.( 3) :The relation between No. of sector versus frequency Fig .(4): The relationship between power transparent and the time for Normal Reticle Fig. (5): The relationship between power transparent and the time for fractal Reticle IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Fig .(6): The MTF versus fc with spot size 0.0003 (Normal Reticle) Fig. (7): The MTF versus fc with spot size 0.0003 (fractal Reticle) Fig .(8): The MTF versus fc with spot size 0.0004(Normal Reticle) Fig. (9): The MTF versus fc with spot size 0.0004(fractal Reticle) IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 ( 2) 2011 Fig .(10): The MTF versus fc with spot size 0.0005(Normal Reticle) Fig. (11): The MTF versus fc with spot size 0.0005(fractal Reticle) Fig. (12): The MTF versus fc with spot size 0.0006(Normal Reticle) Fig. (13): The MTF versus fc with spot size 0.0006(fractal Reticle) 2011) 2( 24مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد التضمین البصري الكسوري في تأثیر حجم البقعة شعبد الرزاق عبد السالم محمد، خالد هالل حربي ،ثائر عبد الكریم خلیل العای جامعة بغداد –كلیة التربیة ابن الهیثم -قسم الفیزیاء 2010، تشرین االول ،30: استلم البحث في 2011، شباط، 27: قبل البحث في الخالصة ة حللت في هذا البحث اإلشارات المنبعثة من قرص التضمین البصري من خالل تغییر حجم بقعة اللیزر الساقط .تردد من خالل مقدار الطاقة النافذة من قرص التضمین البصري فضلاوحسب على القرص قرص التضمین البصري االصدار الثالث الذي یحتوي هطة انشاء برنامج خاص اسمینااجمیع النتائج استحصلت بواس . عشرة منها مضیئة واالخرى معتمة لضوء اللیزر، "امقطع 20جمیع نماذج قرص التضمین تتألف من . العدید من البارمترات .مثل تردد القطع، القدرة النافذة ودالة االنتقال الضمني عدیدة ان عدد المقاطع یعتمد على عوامل ي 0.3یكون حجم بقعة اللیزر ماوقد ثبت عن طریق المحاكاة ان افضل قیمة لدالة االنتقال الضمني تتحقق عند ملم وا .زیادة في حجم المقطع یودي الى انخفاض في قیمة دالة االنتقال الضمني ، دالة االنتقال الضمني التضمین البصري الكسوري ، تردد القطع، حجم المقطع ، القدرة النافذة: كلمات مفتاحیةال